Explore a comprehensive lecture on weight norm inequalities for singular and fractional integral operators in Rn. Delve into the intricacies of this mathematical topic as presented by Ignacio Uriarte-Tuero from the University of Toronto. Learn about A2 and AP weights, the two-way problem and theorem, pivotal conditions, and cancellation conditions. Gain insights into the energy condition, analog testing conditions, and the main theorem's proof. This 58-minute talk, part of the Focus Program on Analytic Function Spaces and their Applications, offers a deep dive into advanced mathematical concepts for those interested in analytic function spaces.